The Villanova Corporation has two different bonds currently outstanding. Bond M

Question

The Villanova Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,200 every six months over the subsequent eight years, and finally pays $1,500 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 10 percent compounded semi-annually, what is the current price of Bond M? of Bond N?

Explanation / Answer

Bond M is slightly more complicated because it involves more cash flows. So basically, we want to find the value today (present value) of all of the cash flows that occur over the 20 year stretch (40 6 month periods) using the interest rate of 5% (10% annual rate but we are concerned with a 6 month interest rate because that's how often interest is compounded).

The easiest way to find this present value is using a cash flow registery of some kind in a financial calculator. We will input the cash flows one at a time, starting with the time period we are concerned with find the NPV (time period 0):

0 CF (time period 0)

0 CF (time period 1)

We then want to let our calculator know that this "0" cash flow is not only occurring once but it is occurring for the first 6 years of the bond's life (12 periods). So we can hit 12 Nj (your specific calculator may be slightly different but you want to let your calculator know that the 0 is happenning 12 times).

Then 1200 CF (for the next 8 years; 16 periods). Again, we must let our caclulator know that this cash flow is occurring 16 times.

Then 1500 CF. This is a little tricky, but even though this cash flow is occurring 12 times we only want to let our calculator know that the cash flow happens 11 times because the 12th cash flow is occurring WITH the 20,000 face value (so we have to lump them together. So after we tell our calculator the cash flow has occurred 11 times we input 21,500 as our final cash flow (20,000 face value + 1500 as the 12th 1500 cash flow).

We then input our interest rate of 5% (remember we use the 6 month rate becuase that's how often interest is compounded).

And our last step is to find NPV in our calculator. When we do that we should get an answer of $13,474.20

Bond N is much easier since there is only one cash flow that we have to discount back; the $20,000 face value. We have to discount it back 40 periods at the 5% interest rate.

To do that we take 20,000/(1.05)^40 and we get $2,840.91

So bond M has a current price of $13,474.20 and bond N has a price of $2,840.91.

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